# EAGLE: Elevating Geometric Reasoning through LLM-empowered Visual Instruction Tuning

arXiv: https://arxiv.org/abs/2408.11397 · HTML: https://mlsanity.com/paper/2408.11397/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 15 of its 62 references that are in the map.
- First posted on arXiv 21 Aug 2024.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)
- Multimodal LLMs / vision-language models / [Embodied and 3D vision-language models](https://mlsanity.com/mllm/embodied-and-3d-vision-language-models/)

## Builds on (most cited first, 15 of 15)

- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Qwen-VL: A Versatile Vision-Language Model for Understanding, Localization, Text Reading, and Beyond](https://mlsanity.com/paper/2308.12966/) (2023)
- [mPLUG-Owl: Modularization Empowers Large Language Models with Multimodality](https://mlsanity.com/paper/2304.14178/) (2023)
- [Gemini: A Family of Highly Capable Multimodal Models](https://mlsanity.com/paper/2312.11805/) (2023)
- [DeepSeek-VL: Towards Real-World Vision-Language Understanding](https://mlsanity.com/paper/2403.05525/) (2024)
- [InternLM-XComposer2: Mastering Free-form Text-Image Composition and Comprehension in Vision-Language Large Model](https://mlsanity.com/paper/2401.16420/) (2024)
- [SPHINX: The Joint Mixing of Weights, Tasks, and Visual Embeddings for Multi-modal Large Language Models](https://mlsanity.com/paper/2311.07575/) (2023)
- [LLaVAR: Enhanced Visual Instruction Tuning for Text-Rich Image Understanding](https://mlsanity.com/paper/2306.17107/) (2023)
- [MathPrompter: Mathematical Reasoning using Large Language Models](https://mlsanity.com/paper/2303.05398/) (2023)
- [Advancing LLM Reasoning Generalists with Preference Trees](https://mlsanity.com/paper/2404.02078/) (2024)
- [Exploring the Reasoning Abilities of Multimodal Large Language Models (MLLMs): A Comprehensive Survey on Emerging Trends in Multimodal Reasoning](https://mlsanity.com/paper/2401.06805/) (2024)
- [Stop Reasoning! When Multimodal LLM with Chain-of-Thought Reasoning Meets Adversarial Image](https://mlsanity.com/paper/2402.14899/) (2024)
- [Describe-then-Reason: Improving Multimodal Mathematical Reasoning through Visual Comprehension Training](https://mlsanity.com/paper/2404.14604/) (2024)

## Built on by (most cited first, 16 of 16)

- [Natural Language Understanding and Inference with MLLM in Visual Question Answering: A Survey](https://mlsanity.com/paper/2411.17558/) (2024)
- [A Survey of Mathematical Reasoning in the Era of Multimodal Large Language Model: Benchmark, Method & Challenges](https://mlsanity.com/paper/2412.11936/) (2024)
- [MM-Verify: Enhancing Multimodal Reasoning with Chain-of-Thought Verification](https://mlsanity.com/paper/2502.13383/) (2025)
- [GeoX: Geometric Problem Solving Through Unified Formalized Vision-Language Pre-training](https://mlsanity.com/paper/2412.11863/) (2024)
- [Euclid: Supercharging Multimodal LLMs with Synthetic High-Fidelity Visual Descriptions](https://mlsanity.com/paper/2412.08737/) (2024)
- [Pi-GPS: Enhancing Geometry Problem Solving by Unleashing the Power of Diagrammatic Information](https://mlsanity.com/paper/2503.05543/) (2025)
- [MathFlow: Enhancing the Perceptual Flow of MLLMs for Visual Mathematical Problems](https://mlsanity.com/paper/2503.16549/) (2025)
- [Position: Reasoning After Perception Means Reasoning Without Vision](https://mlsanity.com/paper/2507.16863/) (2025)
- [A Survey of Deep Learning for Geometry Problem Solving](https://mlsanity.com/paper/2507.11936/) (2025)
- [DRIFT: Transferring Reasoning Priors for Efficient MLLM Fine-Tuning](https://mlsanity.com/paper/2510.15050/) (2025)
- [GeoFM: Enhancing Geometric Reasoning of MLLMs via Synthetic Data Generation through Formal Language](https://mlsanity.com/paper/2510.27448/) (2025)
- [GeoTikzBridge: Advancing Multimodal Code Generation for Geometric Perception and Reasoning](https://mlsanity.com/paper/2603.22687/) (2026)
- [Full spectrum Unlearnable Examples via Spectral Equalization](https://mlsanity.com/paper/2606.26719/) (2026)
- [Geoparsing: Diagram Parsing for Plane and Solid Geometry with a Unified Formal Language](https://mlsanity.com/paper/2604.11600/) (2026)
- [Concise Geometric Description as a Bridge: Unleashing the Potential of LLM for Plane Geometry Problem Solving](https://mlsanity.com/paper/2601.21164/) (2026)
- [Euclid-Omni : A Unified Neuro-Symbolic Framework for Plane Geometry](https://mlsanity.com/paper/2608.14585/) (2026)

## Abstract (arXiv)

Multi-modal Large Language Models (MLLMs) have advanced greatly in general tasks. However, they still face challenges in geometric reasoning, a task that requires synergistic integration of visual recognition proficiency and complex reasoning strength. Existing MLLMs prioritize optimizing the LLM backbone to enhance problem-solving capabilities, while rarely emphasizing improvements in discerning visual elements. However, we reveal that MLLMs suffer from severe visual perception deficiencies, including inaccurate geometric comprehension and severe visual hallucinations, which constrain their reasoning performance. To address this issue, we revisit geometric reasoning through a visual-centric lens that highlights the role of visual perception. To achieve this, we propose EAGLE, a novel coarse-to-fine visual enhancement framework that progressively leverages LLMs' guidance to improve perception proficiency. Specifically, given the substantial disparity between geometric diagrams and natural images, we first introduce Geometric Knowledge Injection. This process explores fundamental knowledge from diagram-caption data to enhance recognition capabilities and improve geometry-language alignments. Then, recognizing that different elements contribute unequally in the reasoning process, we introduce Geometric Knowledge Refinement. This stage leverages LLM-driven chain-of-thought solutions to guide the vision encoder in adaptively prioritizing key elements, fostering a synergistic interplay between visual comprehension and mathematical reasoning. Finally, we develop EAGLE, a geometry expert with strong perception and reasoning capabilities. Extensive experiments demonstrate its effectiveness on three popular benchmarks.